Process algebra with combinators

  • Jan A. Bergstra
  • Inge Bethke
  • Alban Ponse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 832)


We introduce typed combinatory process algebra, a system combining process algebra with types and combinators. We describe its syntax and semantics, and by way of example, verify within this frame-work the Simple Alternating Bit Protocol.

Key Words & Phrases

protocol verification process algebra typed combinatory logic 

1991 Mathematics Subject Classification

69C20 69M10 03B15 03B40 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BB87]
    T. Bolognesi and E. Brinksma. Introduction to the ISO Specification Language LOTOS. Computer Networks and ISDN Systems,14:25–29. Elsevier Science Publishers, 1987.Google Scholar
  2. [BB88]
    J.C.M. Baeten and J.A. Bergstra. Global renaming operators in concrete process algebra. Information and Computation, 78(3):205–245, 1988.CrossRefMathSciNetGoogle Scholar
  3. [BBP93]
    J. A. Bergstra, I. Bethke and A. Ponse. Process algebra with nesting and iteration. Report P9314a (revised version of Report P9314), Programming Research Group, University of Amsterdam, 1994. To appear in The Computer Journal. Google Scholar
  4. [BG93]
    M. Bezem and J. F. Groote. A formal verification of the Alternating Bit Protocol in the Calculus of Constructions. Logic Group Preprint Series, no. 88, Department of Philosophy, University of Utrecht, 1993.Google Scholar
  5. [BK84]
    J.A. Bergstra and J.W. Klop. Process algebra for synchronous communication. Information and Control, 60(1/3):109–137, 1984.MathSciNetGoogle Scholar
  6. [BK85]
    J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77–121, 1985.MathSciNetGoogle Scholar
  7. [BK86]
    J.A. Bergstra and J.W. Klop. Verification of an alternating bit protocol by means of process algebra. In W. Bibel and K.P. Jantke, editors, Math. Methods of Spec. and Synthesis of Software Systems '85, Math, Research 31, pages 9–23, Berlin, 1986. Akademie-Verlag.Google Scholar
  8. [BKO87]
    J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Failures without chaos: a new process semantics for fair abstraction. In M. Wirsing, editor, Formal Description of Programming Concepts — III, Proceedings of the 3 th IFIP WG 2.2 working conference, Ebberup 1986, pages 77–103, Amsterdam, 1987. North-Holland.Google Scholar
  9. [BT84]
    J.A. Bergstra and J.V. Tucker. Top down design and the algebra of communicating processes. Science of Computer Programming, 5(2):171–199, 1984.MathSciNetGoogle Scholar
  10. [BW90]
    J.C.M. Baeten and W.P. Weijland. Process Algebra. Cambridge Tracts in Theoretical Computer Science 18. Cambridge University Press, 1990.Google Scholar
  11. [Bae90]
    J.C.M. Baeten (ed.). Applications of Process Algebra. Cambridge Tracts in Theoretical Computer Science 17. Cambridge University Press, 1990.Google Scholar
  12. [Bri88]
    E. Brinksma. On the design of extended LOTOS — a specification language for open distributed systems. Ph.D. thesis, University of Twente, 1988.Google Scholar
  13. [CF58]
    H. B. Curry and R. Feys. Combinatory Logic. Volume I. North-Holland, Amsterdam, 1958.Google Scholar
  14. [GP90]
    J. F. Groote and A. Ponse. The syntax and semantics of μCRL. Technical Report CS-R9076, CWI, Amsterdam, 1990.Google Scholar
  15. [GP94]
    J. F. Groote and A. Ponse. Proof theory for μCRL: a language for processes with data. In D.J. Andrews, J.F. Groote and C.A. Middelburg, editors, Proceedings of the International Workshop on Semantics of Specification Languages. Workshops in Computer Science, Springer Verlag, 1994.Google Scholar
  16. [GV93]
    R.J. van Glabbeek and F.W. Vaandrager. Modular specifications in Process Algebra. Theoretical Computer Science, 113(2):294–348, 1993.Google Scholar
  17. [HS86]
    J. R. Hindley and J. P. Seldin. Introduction to combinators and λ-calculus. London Mathematical Society Student Texts.1, Cambridge University Press, Cambridge, 1986.Google Scholar
  18. [MV90]
    S. Mauw and G. J. Veltink. A process specification formalism. Fundamenta Informaticae, XIII:85–139, 1990.Google Scholar
  19. [Mau91]
    S. Mauw. A process specification formalism. Ph.D. thesis, University of Amsterdam, 1991.Google Scholar
  20. [Par85]
    J. Parrow. Fairness properties in process algebra — with applications in communication protocol verification. Ph.D. thesis, Dept. of Comp. Sci., Uppsala Univ., 1985.Google Scholar
  21. [San67]
    L. E. Sanchis. Functionals defined by recursion. Notre Dame Journal of Formal Logic, VIII(3):161–174, 1967.MathSciNetGoogle Scholar
  22. [Sch24]
    M. Schönfinkel. Über die Bausteine der mathematischen Logik. Mathematische Annalen, 92:305–316, 1924.CrossRefMATHMathSciNetGoogle Scholar
  23. [Vaa90]
    F. W. Vaandrager. Two simple protocols. In J. C. M. Baeten, editor, Applications of Process Algebra, pages 23–44, Cambridge Tracts in Theoretical Computer Science 17, Cambridge University Press, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jan A. Bergstra
    • 1
    • 2
  • Inge Bethke
    • 2
    • 3
  • Alban Ponse
    • 1
  1. 1.Programming Research GroupUniversity of AmsterdamSJ AmsterdamThe Netherlands
  2. 2.Department of PhilosophyUtrecht UniversityCS UtrechtThe Netherlands
  3. 3.Department of Software TechnologyCWISJ AmsterdamThe Netherlands

Personalised recommendations